The basis of the set of polynomials with degree at most n

In my book it says that the basis of the set of polynomials of degree at most n ie
K[x
]
≤n
has the basis
1,x,
x
2
,...,
x
n
. But arent
x,
x
2
,...
a linear combination of each other? This confuses me since the set isnt a set of vectors here.

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